Blender Saves game as .blend when exporting as runtime,
You're probably exporting it wrong. Make sure you have the save as runtime addon enabled (User preferences>Addons>Game Engine). Without this you can't export as a game runtime, meaning people can't play it, like the issue you described. 



Once that's done, make sure you are viewing the FIRST SCREEN you want the player to see. Splash screen, main menu, level 1, etc. When exporting, the scene you are currently viewing will be the first thing players see. Also make sure you have selected "Blender Game" under render engine options. Then you're good to export it.

NOTE: I'm on Windows, but should be the same with Linux, part from the .exe obviously.



Hope this helps.